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This is a Cohort Study study (also classified as: Experimental Study).

October 3, 2025Open Access

Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence

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Depth preservation allows harmonic-analytic results to be transferred from characteristic 0 to characteristic p, enhancing the understanding of local langlands correspondence.
For nonarchimedean local fields, we prove an equivalence of Bernstein blocks for connected reductive groups between fields of different characteristics.
The method involves a block-by-block comparison of structures between groups defined over fields of varying characteristics, providing deeper insights into their properties.
These results facilitate working in characteristic 0 without losing generality for a wide range of harmonic analysis applications in p-adic groups.

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The revised depth notion preserves characteristics in local langlands correspondence, indicating broad applications in harmonic analysis.

Manish Mishra (2025) studied this question.

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